Magic Mushrooms appear when you use your machete to expand the borders of your town. They always appear with smaller Strange Mushrooms around them. If you find some Strange Mushrooms at the border of your town, then you should explore nearby to find the Magic Mushroom.
Magic Mushrooms take one hour to be harvested to get 104 Wood and 15 XP, but unlike other mushrooms, they will regrow (in the same location) after another hour. This will provide you with a steady supply of Wood for building.